The surface of an cube is 96cm what is the area of one of its faces?

SA = 6*s^2   there are six sides on a cube all equal with the area equalling s^2

96 = 6s^2   divide by 6

16 = s^2

s=4

The area of one of the faces is 4^2 = 16 cm ^2

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4